From black-box complexity to designing new genetic algorithms
Black-box complexity theory recently produced several surprisingly fast black-box optimization algorithms. In this work, we exhibit one possible reason: These black-box algorithms often profit from solutions inferior to the previous-best. In contrast, evolutionary approaches guided by the “survival...
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| Veröffentlicht in: | Theoretical computer science Jg. 567; S. 87 - 104 |
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| Sprache: | Englisch |
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Elsevier B.V
16.02.2015
Elsevier |
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | Black-box complexity theory recently produced several surprisingly fast black-box optimization algorithms. In this work, we exhibit one possible reason: These black-box algorithms often profit from solutions inferior to the previous-best. In contrast, evolutionary approaches guided by the “survival of the fittest” paradigm often ignore such solutions. We use this insight to design a new crossover-based genetic algorithm. It uses mutation with a higher-than-usual mutation probability to increase the exploration speed and crossover with the parent to repair losses incurred by the more aggressive mutation. A rigorous runtime analysis proves that our algorithm for many parameter settings is asymptotically faster on the OneMax test function class than all what is known for classic evolutionary algorithms. A fitness-dependent choice of the offspring population size provably reduces the expected runtime further to linear in the dimension. Our experimental analysis on several test function classes shows advantages already for small problem sizes and broad parameter ranges. Also, a simple self-adaptive choice of these parameters gives surprisingly good results. |
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| AbstractList | Black-box complexity theory recently produced several surprisingly fast black-box optimization algorithms. In this work, we exhibit one possible reason: These black-box algorithms often profit from solutions inferior to the previous-best. In contrast, evolutionary approaches guided by the “survival of the fittest” paradigm often ignore such solutions. We use this insight to design a new crossover-based genetic algorithm. It uses mutation with a higher-than-usual mutation probability to increase the exploration speed and crossover with the parent to repair losses incurred by the more aggressive mutation. A rigorous runtime analysis proves that our algorithm for many parameter settings is asymptotically faster on the OneMax test function class than all what is known for classic evolutionary algorithms. A fitness-dependent choice of the offspring population size provably reduces the expected runtime further to linear in the dimension. Our experimental analysis on several test function classes shows advantages already for small problem sizes and broad parameter ranges. Also, a simple self-adaptive choice of these parameters gives surprisingly good results. |
| Author | Ebel, Franziska Doerr, Carola Doerr, Benjamin |
| Author_xml | – sequence: 1 givenname: Benjamin surname: Doerr fullname: Doerr, Benjamin organization: École Polytechnique, Palaiseau, France – sequence: 2 givenname: Carola surname: Doerr fullname: Doerr, Carola organization: Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, Paris, France – sequence: 3 givenname: Franziska surname: Ebel fullname: Ebel, Franziska organization: Saarland University, Saarbrücken, Germany |
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| Keywords | Heuristic search Theory of randomized search heuristics Runtime analysis Genetic algorithms Black-box complexity |
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| Snippet | Black-box complexity theory recently produced several surprisingly fast black-box optimization algorithms. In this work, we exhibit one possible reason: These... |
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| SubjectTerms | Algorithms Asymptotic properties Black-box complexity Computer Science Crossovers Evolutionary Genetic algorithms Heuristic search Mathematical analysis Mathematical models Mutations Neural and Evolutionary Computing Run time (computers) Runtime analysis Theory of randomized search heuristics |
| Title | From black-box complexity to designing new genetic algorithms |
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